Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the classical Ito stochastic calculus. The existence result is based on the Yamada-Watanabe theorem.Comment: 21 page

The connection between stellar mass, age and quenching timescale in massive quiescent galaxies at z≃1z \simeq 1

We present a spectro-photometric study of a mass-complete sample of quiescent galaxies at $1.0 < z < 1.3$ with $\mathrm{log_{10}}(M_{\star}/\mathrm{M_{\odot}}) \geq 10.3$ drawn from the VANDELS survey, exploring the relationship between stellar mass, age and star-formation history. Within our sample of 114 galaxies, we derive a stellar-mass vs stellar-age relation with a slope of $1.20^{+0.28}_{-0.27}$ Gyr per decade in stellar mass. When combined with recent literature results, we find evidence that the slope of this relation remains consistent over the redshift interval $0<z<4$. The galaxies within the VANDELS quiescent display a wide range of star-formation histories, with a mean star-formation timescale of $1.5\pm{0.1}$ Gyr and a mean quenching timescale of $1.4\pm{0.1}$ Gyr. We also find a large scatter in the quenching timescales of the VANDELS quiescent galaxies, in agreement with previous evidence that galaxies at $z \sim 1$ cease star formation via multiple mechanisms. We then focus on the oldest galaxies in our sample, finding that the number density of galaxies that quenched before $z = 3$ with stellar masses $\mathrm{log_{10}}(M_{\star}/\mathrm{M_{\odot}}) \geq 10.6$ is $1.12_{-0.72}^{+1.47} \times 10^{-5} \ \mathrm{Mpc}^{-3}$. Although uncertain, this estimate is in good agreement with the latest observational results at $3<z<4$, tentatively suggesting that neither rejuvenation nor merger events are playing a major role in the evolution of the oldest massive quiescent galaxies within the redshift interval $1<z<3$.Comment: Accepted for publication in MNRAS, 11 pages, 6 figure

A first look at JWST CEERS: massive quiescent galaxies from 3 < z < 5

We report a robust sample of 9 massive quiescent galaxies at redshift, $z > 3$, selected using the first data from the JWST CEERS programme. Three of these galaxies are at $4 < z < 5$, constituting the best evidence to date for quiescent galaxies significantly before $z=4$. These extreme galaxies have stellar masses in the range log$_{10}(M_*/$M$_\odot) = 10.5-11.3$, and formed the bulk of their mass at $6 < z < 9$, with two objects having star-formation histories that suggest they had already reached log$_{10}(M_*/$M$_\odot) > 10$ by $z\simeq8$. We report number densities for our sample, demonstrating that previous work underestimated the number of quiescent galaxies at $3 < z < 4$ by at least a factor of $3-6$, due to a lack of ultra-deep imaging data at $\lambda>2\,\mu$m. This result deepens the existing tension between observations and theoretical models, which already struggle to reproduce previous estimates of $z>3$ quiescent galaxy number densities. Upcoming wider-area JWST imaging surveys will provide larger samples of such galaxies, as well as providing opportunities to search for quiescent galaxies at $z>5$. The galaxies we report are excellent potential targets for JWST NIRSpec spectroscopy, which will be required to understand in detail their physical properties, providing deeper insights into the processes responsible for quenching star formation during the first billion years.Comment: 11 pages, 6 figures, submitted to MNRA

The evolution of the galaxy UV luminosity function at redshifts z ~ 8-15 from deep JWST and ground-based near-infrared imaging

International audienceWe reduce and analyse the available JWST ERO and ERS NIRCam imaging (SMACS0723, GLASS, CEERS) in combination with the latest deep ground-based near-infrared imaging in the COSMOS field (provided by UltraVISTA DR5) to produce a new measurement of the evolving galaxy UV luminosity function (LF) over the redshift range z = 8 - 15. This yields a new estimate of the evolution of UV luminosity density (ρUV), and hence cosmic star formation rate density (ρSFR) out to within UV (and thus ρSFR), continues to decline gradually and steadily up to z ~ 15 (as anticipated from previous studies which analysed the pre-existing data in a consistent manner to this study). We provide details of the 61 high-redshift galaxy candidates, 47 of which are new, that have enabled this new analysis. Our sample contains 6 galaxies at z ≥ 12, one of which appears to set a new redshift record as an apparently robust galaxy candidate at z ≃ 16.4, the properties of which we therefore consider in detail. The advances presented here emphasize the importance of achieving high dynamic range in studies of early galaxy evolution, and re-affirm the enormous potential of forthcoming larger JWST programmes to transform our understanding of the young Universe

Evidence for the emergence of dust-free stellar populations at z > 10

We present an analysis of the UV continuum slopes for a sample of $176$ galaxy candidates at $8 < z_{\mathrm{phot}} < 16$. Focusing primarily on a new sample of $125$ galaxies at $\langle z \rangle \simeq 11$ selected from $\simeq 320$ arcmin$^2$ of public JWST imaging data across $15$ independent datasets, we investigate the evolution of $\beta$ in the galaxy population at $z > 8$. In the redshift range $8 < z < 10$, we find evidence for a relationship between $\beta$ and $M_{\rm UV}$, such that galaxies with brighter UV luminosities display redder UV slopes, with $\rm{d}\beta/ \rm{d} M_{\rm UV} = -0.17 \pm 0.03$. A comparison with literature studies down to $z\simeq2$ suggests that a $\beta-M_{\rm UV}$ relation has been in place from at least $z\simeq10$, with a slope that does not evolve strongly with redshift, but with an evolving normalisation such that galaxies at higher redshifts become bluer at fixed $M_{\rm UV}$. We find a significant trend between $\beta$ and redshift, with the inverse-variance weighted mean value evolving from $\langle \beta \rangle = -2.17 \pm 0.05$ at $z = 9.5$ to $\langle \beta \rangle = -2.56 \pm 0.05$ at $z = 11.5$. Based on a comparison with stellar population models, we find that at $z>10.5$ the average UV continuum slope is consistent with the intrinsic blue limit of `dust-free' stellar populations $(\beta_{\mathrm{int}} \simeq -2.6)$. These results suggest that the moderately dust-reddened galaxy population at $z < 10$ was essentially dust free at $z \simeq 11$. The extremely blue galaxies being uncovered at $z>10$ place important constraints on the dust content of early galaxies, and imply that the already observed galaxy population is likely supplying an ionizing photon budget capable of maintaining ionized IGM fractions of $\gtrsim 5$ per cent at $z\simeq11$.Comment: 16 pages, 12 figures, submitted to MNRA

A combined VANDELS and LEGA-C study: the evolution of quiescent galaxy size, stellar mass, and age from z = 0.6 to z = 1.3

We study the relationships between stellar mass, size and age within the quiescent population, using two mass-complete spectroscopic samples with $\mathrm{log_{10}}(M_{\star}/\mathrm{M_{\odot}})>10.3$, taken from VANDELS at $1.0<z<1.3$, and LEGA-C at $0.6<z<0.8$. Using robust D$_{n}$4000 values, we demonstrate that the well-known 'downsizing' signature is already in place by $z\simeq1.1$, with D$_{n}$4000 increasing by $\simeq0.1$ across a $\simeq$ 1 dex mass interval for both VANDELS and LEGA-C. We then proceed to investigate the evolution of the quiescent galaxy stellar mass-size relation from $z\simeq1.1$ to $z\simeq0.7$. We find the median size increases by a factor of $1.9\pm{0.1}$ at $\mathrm{log_{10}}(M_{\star}/\mathrm{M_{\odot}})=10.5$, and see tentative evidence for flattening of the relation, finding slopes of $\alpha=0.72\pm0.06$ and $\alpha=$ $0.56\pm0.04$ for VANDELS and LEGA-C respectively. We finally split our sample into galaxies above and below our fitted mass-size relations, to investigate how size and D$_{n}$4000 correlate. For LEGA-C, we see a clear difference, with larger galaxies found to have smaller D$_{n}$4000 at fixed stellar mass. Due to the faintness and smaller numbers of the VANDELS sample, we cannot confirm whether a similar relation exists at $z\simeq1.1$. We consider whether differences in stellar age or metallicity are most likely to drive this size-D$_{n}$4000 relation, finding that any metallicity differences are unlikely to fully explain the observed offset, meaning smaller galaxies must be older than their larger counterparts. We find the observed evolution in size, mass and D$_{n}$4000 across the $\simeq2$ Gyr from $z\sim1.1$ to $z\sim0.7$ can be explained by a simple toy model in which VANDELS galaxies evolve passively, whilst experiencing a series of minor mergers.Comment: 14 pages, 9 figures, submitted to MNRA